Single Allocation P-hub Median Problem Research Articles

An artificial immune system algorithm for solving the uncapacitated single allocation p-Hub median problem

The present paper deals with a variant of hub location problems (HLP): the uncapacitated single allocation p-Hub median problem (USApHMP). This problem consists to jointly locate hub facilities and to allocate demand nodes to these selected facilities. The objective function is to minimize the routing of demands between any origin and destination pair of nodes. This problem is known to be NP-hard. Based on the artificial immune systems (AIS) framework, this paper develops a new approach to efficiently solve the USApHMP. The proposed approach is in the form of a clonal selection algorithm (CSA) that uses appropriate encoding schemes of solutions and maintains their feasibility. Comprehensive experiments and comparison of the proposed approach with other existing heuristics are conducted on benchmark from civil aeronautics board, Australian post, PlanetLab and Urand data sets. The results obtained allow to demonstrate the validity and the effectiveness of our approach. In terms of solution quality, the results obtained outperform the best-known solutions in the literature.

Consolidation Model Recommendation for Rice Distribution in Indonesian Bureau of Logistics (West Java Regional Division)

BULOG (Indonesian Bureau of Logistics) Regional Division West Java is a state-owned public company that regulates and maintains a supply of rice in order to meet the needs of all Indonesian people. Currently, BULOG distributing rice from one SubDivre warehouse to another SubDivre warehouse (point-to-point system) so shipping costs are higher because the frequency of transportation used is higher and the total distance traveled is higher. To reduce the cost of distribution, we propose consolidation model based on hub and spoke network topology. Hub and spoke system is done by determining which points become the hubs and which points become the spoke. The problem in determining the location of the hub and spoke is known as the hub location problem. In this problem, single allocation p-hub median problem is used. We use AMPL to get the solution. Various number of hubs (5,6,7) are tested and evaluated based on total shipping cost. The number of hubs which gives the minimum total shipping cost is 7. Delivery system using the hub and spoke network model can reduce the total cost of distribution by 13,94%.

An efficient heuristic for a hub location routing problem

This paper examines a new model for hub location known as the hub location routing problem. The problem shares similarities with the well studied uncapacitated single allocation p-hub median problem except that the hubs are now connected to each other by a cyclical path (or tour) known as the global route, each cluster of non-hub nodes and assigned hub is also connected by a single tour known as a local route, and the length of the local routes is constrained to a maximum number of nodes. Thus, aside from the normal tasks of hub selection and allocation of non-hub nodes, up to p + 1 travelling salesman problems need to be solved. A heuristic based on the general variable neighborhood search framework is proposed here to solve this very complicated problem. The improvement phase of the algorithm uses a sequential variable neighborhood descent with multiple neighborhoods required to suit the complex nature of the problem. A best sequencing of the neighborhoods is established through empirical testing. The perturbation phase known as the shaking procedure also uses a well-structured selection of neighborhoods in order to effectively diversify the search to different regions of the solution space. Extensive computational testing shows that the new heuristic significantly outperforms the state-of-the-art. Out of 912 test instances from the literature, we are able to obtain 691 new best known solutions. Not only are the improvements in objective values quite impressive, but also these new solutions are obtained in a small fraction of the time required by the competing algorithms.

The hub location’s method for solving optimal control problems

In this paper, the p-hub median’s algorithm is modified to find an approximate solution of bounded continuous-time nonlinear optimal control problems (NOCP). For this purpose, after presenting the similarities between uncapacitated single allocation p-Hub median problem (USApHMP) which is a special case of the well-studied hub location problem and a discretized form of NOCP, an improvement on sequential general variable neighborhood search algorithm (SGVNS) is proposed. This algorithm that denoted as new-sequential general variable neighborhood search (N-SGVNS) is based on three local searches that use efficient neighborhood interchange. In addition, comparing the NOCP with the USApHMP has led us to introduce a suitable method to find an approximate solution for NOCP. Our results of the implementation of the N-SGVNS on the real-world data set for the USApHMP show the high accuracy of the obtained solutions. Because of the proposed algorithm is able to solve the USApHMP successfully, we hoped that this method would also be successful for NOCP. Solving of benchmark NOCP and then comparing the results of the N-SGVNS with recently developed algorithms suggest that the presented strategy may provide an outstanding framework for designing cost-effective control functions.

Robust single allocation p-hub median problem under hose and hybrid demand uncertainties: models and algorithms

ABSTRACT Hub location problem is one of the extensively studied and important problems in the field of facility location and network design with numerous applications in transportation, postal services, and telecommunications. In this paper, we address the robust single allocation p-hub median problem under polyhedral demand uncertainty. The origin-destination (O/D) flow values are assumed to be uncertain and are modeled as two different polyhedral uncertainty sets, called the hose and the hybrid uncertainty sets. The problems are formulated as linear MIP models and matheuristic solution algorithms based on Tabu Search (TS) are developed for solving them. Computational experiments show the capability of the proposed algorithms to solve the real-world instances of the problem in small computational times. Furthermore, the effect of different input parameters on the final solutions are studied.

A single allocation p-hub median problem with general piecewise-linear costs in arcs

Hubs are used in postal, air passenger transportation, and less-than-truckload (LTL) transportation industries to consolidate, sort, and classify the flows from multiple origins to multiple destinations (OD pairs). Hub-and-spoke networks are commonly designed to exploit economies of scale, and multiple cost functions have been proposed. Hub Location Problems have been used extensively to design hub-and-spoke networks.Notwithstanding the previous efforts in developing accurate cost functions in hub location problems, there is no as today a model flexible enough to represent various practical cost curves. To address this gap, we propose a single-allocation p-hub location problem, in which the cost of the flow on any arc of the network is modeled as a general piecewise-linear function. Inspired by the parcel delivery industry, we allow the existence of routes containing more than three arcs, i.e., any single route may use more than two hubs.The resulting model is hard to solve, even for small instances. We propose a math-heuristic (i.e., a heuristic with exact mathematical programming components), which allows us to solve instances with up to 200 nodes. We obtain solutions considering different cost functions, showing the stability and scalability of the model. Our experiments reveal the dependence between the cost function considered and both hub location and node allocation.

Benders Decomposition Algorithms for Two Variants of the Single Allocation Hub Location Problem

The hub location problem (HLP) is a special type of the facility location problem with numerous applications in the airline industry, postal services, and computer and telecommunications networks. This paper addresses two basic variants of the HLP, namely the uncapacitated single allocation hub location problem (USAHLP) and the uncapacitated single allocation p-hub median problem (USAp HMP). Exact solution procedures based on Benders decomposition algorithm are proposed to tackle large sized instances of these problems. The standard Benders decomposition algorithm is enhanced through implementation of several algorithmic refinements such as using a new cut disaggregation scheme, generating strong optimality cuts, and an efficient algorithm to solve the dual subproblems. Furthermore, a modern implementation of the algorithm is used where a single search tree is established for the problem and Benders cuts are successively added within a branch-and-cut framework. Extensive computational experiments are conducted to examine the efficiency of the proposed algorithms. We have been able to solve all the instances of the problems from all three main data sets of the HLP to optimality in reasonable computational times.

Solving Single Allocation Hub Location Problems on Euclidean Data

If shipments have to be transported between many sources and sinks, direct connections from each source to each sink are often too expensive. Instead, a small number of nodes are upgraded to hubs that serve as transshipment points. All sources and sinks are connected to these hubs, so that only a few, strongly consolidated transport relations exist. While hubs and detours lead to additional costs, the savings from bundling shipments—i.e., economies of scale—usually outweigh these costs. Typical applications for hub networks are in cargo, air freight, and postal and parcel transport services. In this paper, we consider three classical and two recent formulations of single allocation hub location problems—i.e., hub location problems in which every source and sink is connected to exactly one hub. Solving larger instances of these problems to optimality is difficult because the inherent quadratic structure of the problem has to be linearized: This leads to a sharp rise in the number of variables. Our new approach relies on the fact that many instances—including the Civil Aeronautics Board and Australian Post data sets—have a Euclidean structure: The distances between the possible hub locations are Euclidean. This enables us to construct a new linearization together with a row generation procedure that solves instances of up to 200 nodes to optimality. For problems like the uncapacitated single allocation p-hub median problem and the uncapacitated single allocation hub location problem, we present the first optimal results for instances of this size.

Freight network design with heterogeneous values of time

Abstract This paper aims to demonstrate the effect of recognizing heterogeneity in values of time on the design of a hub network for freight transportation. By taking the VOT distribution into account, we emphasize shippers’ broader logistical, social and economic situation in the network design, and are not limited to commodity types. The paper employs the single allocation p-hub median problem which minimizes the total generalized transportation cost (time, distance, etc.) with given demands. VOT is assumed to be discretely distributed, and estimated by mean-dispersion model and Latent Class model, based on a Stated Preference survey conducted in China, investigating railway shippers’ choice behavior of railway services. A local railway network with 14 nodes and 20 linkages is applied to discuss the effect of VOT distribution on multiple (i.e., 3) hub location strategy. Simulated Annealing (SA) is designed to solve the single allocation p-hub median problems. The numerical results shows that the VOT and its distribution should be taken into account for better simulating railway shippers’ heterogeneous valuations of service time versus time.

Robust bi-objective optimization of uncapacitated single allocation p-hub median problem using a hybrid heuristic algorithm

The p-hub median problem aims at locating p-hub facilities in a network and allocating non-hub nodes to the hubs such that the overall transportation cost is minimized. One issue of major importance in this problem remarks the requirement to deal with uncertain factors such as weather conditions and traffic volume. These lead to uncertainty in travel time between origin and destination points. In today's competitive markets in which customers look for robust delivery services, it is important to minimize the upper bound of uncertainty in the network routes. In this paper, a robust bi-objective uncapacitated single allocation p-hub median problem (RBUSApHMP) is introduced in which travel time has non-deterministic nature. The problem aims to select location of the hubs and allocation of the other nodes to them so that overall transportation cost and maximum uncertainty in network are minimized. To do this, a desirability function-based approach is suggested that ensures both interested objectives to fall within their specification limits. Due to the complexity of the model, a heuristic based on scatter search and variable neighborhood descent is developed. To evaluate the performance of the proposed method a computational analysis on Civil Aeronautics Board and Australian Post data sets was performed. The obtained results using the proposed hybrid metaheuristic are compared to those of the optimum solutions obtained using GAMS. The results indicate excellent performance of the suggested solution procedure to optimize RBUSApHMP.

Lower Bounding Procedures for the Single Allocation Hub Location Problem

This paper proposes a new lower bounding procedure for the Uncapacitated Single Allocation p-Hub Median Problem based on Lagrangean relaxation. For solving the resulting Lagrangean subproblem, the given problem structure is exploited: it can be decomposed into smaller subproblems that can be solved efficiently by combinatorial algorithms. Our computational experiments for some benchmark instances demonstrate the strength of the new approach.

Reactive GRASP for the Capacitated Single Allocation p-Hub Median Problem

In this paper the authors consider a capacitated single allocation p-hub median problem (CSApHMP) which is to determine the location of p hubs, the allocation of non-hub nodes to hubs in the logistics network. This problem is formulated as an integer programming model with the objective of minimizing the sum of total transportation cost and fixed cost of the selected p hubs. Since the CSApHMP is NP-hard, it is difficult to obtain optimal solution within a reasonable computational time with exact solution approach. The authors only solve the CSApHMP using Gurobi optimizer for the small sized problems. A reactive greedy randomized adaptive search procedure (GRASP) is proposed to solve the problem. To illustrate the effectiveness of the proposed reactive GRASP algorithm, a comparative study from the benchmark instances is also presented. The experimental results show that the proposed GRASP heuristic can be an effective solution method for the capacitated hub location problem.

Endogenous Effects of Hubbing on Flow Intensities

Location of hub facilities and the allocation decisions in transport networks endogenously affect both the flow intensities and the transportation costs. Since the introduction of the hub location problem to the operations research literature in mid- 1980s, many researchers investigated different ways of modelling the effects of hub facilities on the transportation costs. On the other hand, there has been very limited research on their effect on the flow intensities. This study proposes a new approach, inspired by the Bass diffusion model, to forecast the change in the demand patterns generated at different locations as a result of the placement of new hubs. This new model is used in the context of the uncapacitated single allocation p-hub median problem to investigate the effects of endogenous attraction, caused by the spatial interaction of present hubs, on future hub location decisions. Computational results indicate that the location and allocation decisions may be greatly affected when these forecasts are taken into account in the selection of future hub locations.

A fast variable neighborhood search for p-hub median problem using social network analysis concepts

This study will contribute to the uncapacitated single allocation p-hub median problem (USApHMP) which is known as an NP-hard problem in the literature. This problem is concerned with locating of hub facilities in a network and allocating of each non-hub node to just one hub in order to minimize total transportation costs in the network. A hybrid variable neighborhood search (VNS) algorithm is proposed considering three structures of local search which are used as a combination of nested VNS and sequential VNS in the algorithm. For reduction of the dimensions in the nested part, social network analysis centrality measures for the node are used to choose elite points instead of all existing points in the local search structures. The obtained results demonstrate that this will not only retain quality of the solutions, but also reduce run time of the algorithm significantly. Three standard data sets (AP, CAB, and URAND) were used for numerical analysis. Computational results show that quality of the obtained solutions is good and able to compete with other heuristics addressed in the literature. From the viewpoint of execution time, it considerably outperforms all other algorithms. The intelligent search embedded in this algorithm makes it robust and efficient on networks with up to 400 nodes.

Meta-heuristic solution approaches for robust single allocation p-hub median problem with stochastic demands and travel times

Hub location problems appear at the core of strategic planning for many transportation and logistics problems. This class of optimization problems has received a wide gamut of research attention during the last few decades. However, the associated mathematical formulations are mainly developed with deterministic parameters to avoid the complexities and computational difficulties. In this paper, we put forward an extension to the uncapacitated single allocation p-hub median problem under uncertainty in which demands and travel times are stochastic. A robust optimization approach is used to deal with uncertainty in parameters and design a robust hub-and-spoke network. The developed model minimizes the total expected transportation costs, while bounding the relative regret in each scenario. To efficiently solve the model, a two-stage approach is investigated to design two hybrid heuristics. We firstly apply a meta-heuristic (i.e., variable neighborhood search (VNS) or particle swarm optimization (PSO)) to find the best combination for the hubs location. Then, by fixing the hubs location, the original model easily decomposes by scenario for which an efficient tabu search (TS) is designed. Encouraging results on a wide-range of test problems are reported.

Unmanned Aerial Vehicle hub-location and routing for monitoring geographic borders

Recently, hub location problems have become more common with successful applications in air transportation. In this paper, we consider a hub-location and routing problem for border (Borders in this work refer to land borders, unless otherwise stated.) security in Turkey. Security is currently one of the most important issues. Countries are spending large amounts to prevent threats that may come from neighboring countries. Land borders are required to be monitored because of illegal border crossing activities and terrorist attacks. Various geographical restrictions at the borders can cause difficulties in monitoring and gathering the required data. We focus on selecting hubs among the airports run by the General Directorate of State Airports Authority of Turkey, the assignment of demand points to hubs and determining optimal routes for each hub. The study consists of two stages. First, the single allocation p-hub median problem is solved to determine the locations of the hubs for unmanned aircraft. To select hubs, the decision model uses an appropriateness parameter that is obtained by using ELECTRE, a multi-criteria decision-making tool. Five criteria are considered: The type of airport, the remoteness from threats, the proximity to a land border, the aerodrome traffic density and the time that the possible hubs are open to the air traffic. In the second stage, optimal routes are determined for each hub by using two mathematical models. The first model is cost-oriented and there is one vehicle per hub. In the second mathematical model for routing, the monitoring frequency parameters which means the priority of monitoring of the demand nodes obtained by using ELECTRE are used to maximize the monitoring frequency of the demand nodes. The criteria for demand nodes are (1) the need for UAVs, (2) illegal border crossing, and (3) the number of the illegal border activities and attacks. There are three vehicles per hub in the second model. The results of two mathematical models for routing problem are evaluated.

Lagrangian Relaxation for the Capacitated Single Allocation p-Hub Median Problem

In this paper the authors consider a capacitated single allocation p-hub median problem (CSApHMP). The authors determine the location of p hubs, the allocation of non-hub nodes to hubs in the network. This problem is formulated as 0-1 integer programming model with the objective of the minimum total transportation cost and the fixed cost associated with the establishment of hubs. Optimal solutions are obtained using Gurobi optimizer for the small sized problems. Since the CSApHMP is NP-hard, it is difficult to obtain an optimal solution within a reasonable computational time. Therefore, a Lagrangian relaxation (LR) heuristic is developed to solve the problem. The LR performance is examined through a comparative study. The experimental results show that the proposed LR heuristic can be a viable solution method for the capacitated hub and spoke network design problem.

A New Approach to Single Allocation Hub Location Problem and An Application in The Air Cargo Transportation

In this study, the new constraints which can be applied in network design problem are developed by taking especially the sectoral features of air transportation and aircraft types into consideration. A new mixed integer linear programming model is developed by including the new constraints into the traditional model of uncapacitated single allocation p-hub median problem accordingly. The aim of this study is to analyze the effects of the new constraints on the hub location. The model is tested by using Turkish air cargo statistics and the data related to the aircraft types, A300-B4 and F27-500. The results of the analysis show that the new constraints and the aircraft types used in air cargo transportation have the significant effects on the hub location problem.

A Hierarchical Approach to the Capacitated Single Allocation <i>p</i>-Hub Median Problem with Direct Shipment

In this paper we consider a capacitated single allocation p-hub median problem with direct shipment (CSApHMPwD). We determine the location of p hubs, the allocation of non-hub nodes to hubs, and direct shipment paths in the network. This problem is formulated as 0-1 integer programming model with the objective of the minimum total transportation cost and the fixed cost associated with the establishment of hubs. An optimal solution is found using CPLEX for the small sized problems. Since the CSApHMPwD is NP-hard, it is difficult to obtain optimal solution within a reasonable computational time. Therefore, an ant colony optimization algorithm is developed which solves hub selection and node allocation problem hierarchically. Its performance is examined through a comparative study. The experimental results show that the proposed ant colony optimization algorithm can be a viable solution method for the capacitated hub and spoke network design problem.

An improved linearization technique for a class of quadratic 0-1 programming problems

The recent research on linearization techniques for solving 0-1 quadratic programming problems focuses on providing concise models and tightening constraint bounds. In this paper, we propose a computational enhancement for a linearization technique to make the linearized model much faster to solve. We investigate the computational performance of the proposed approach, by comparing it with other linearization techniques on a class of 0-1 quadratic programming problems. We can further speed up the proposed technique by heuristically tightening the constraint bounds, as demonstrated by solving the uncapacitated single allocation p-hub median problem using the Civil Aeronautics Board data.